The downside is, of course, the cost-differential of staying at campgrounds or motels etc. This is the sweet spot I'm trying to find ... literally might even be worth what I mentioned before about literally going into "The woods" and pitching a tent.
The locale you choose to be in will have a large effect on all of this. There are areas where the motels are generally dirt cheap. There are areas where camping for free in plain sight is easy. There are areas that offer very cheap camping in great state parks.
In the middle of the country in the great plains I have many times stayed overnight in town parks often sleeping under the shelter of a picnic pavilion. I have never been run off despite having done this many times. I suspect that staying multiple nights would be likely to get you run off. If the town is large enough to have a library or fast food establishment there is probably WiFi.
In Oregon, California and some other places cheap camping is generally available to cyclists. In many cases long stays will not be allowed. You might have to go into town to do any connected work unless you can manage with 3G or 4G assuming there is a signal, and there often will not be.
On my Southern Tier tour, I met a guy who said he was walking across the country carrying his gear in a double baby jogger. He had been doing so for quite a few years and apparently was not planning to get there any time soon. He stopped for weeks or months at a time where ever he felt like it. When I camped next to him he had been staying for quite a few weeks at a $10 a night campsite at the Apache Gold Casino. The price was cheap, the food in the casino was both good and cheap, and they probably had WiFi.
Personally I prefer to go home at the end of a tour. A few weeks or a few month on the road is nice, but doing it full time all year long would get old for me. I suggest doing a long tour with a planned end, maybe do something like the Trans America, Southern Tier, or Northern Tier routes. It is an easier way to break into life on the road because others have already blazed the trail for you. By the end of a trip of that length you will know whether life on the road full time is for you. You will also have learned the ropes and know what does and does not work for you.